Math
posted by excel .
1a) Prove that there exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2
1b) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational
1c) prove that if 2^√2is irrational then √2^√2is irrational.
Thanks for your help.

(√2^√2)^√2 = √2^(√2*√2) = √2^2 = 2
√2^√2 = (2^1/2)^√2 = 2^(1/√2)
That should get you started
Respond to this Question
Similar Questions

Math
Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3xy=1 and x+y=2. a. (3√2 +√10)x(√10 + √2)y2√10+√2=0 b. (3√2  √10)x+(√10  √2)y+2√10+√2=0 … 
irrational numbers?!
what are rational and irrational numbers? 
algebra/trig
1. which number below is irrational? a)√4/9 b) √20 c)√121 Why is the number you chose irrational? 
Algebra
Order the following numbers from least to greatest. √5, 0.1, (5/3), 0.7, √2 a. 0.7, √2, (5/3), √5, 0.1 b. √5, √2, 0.7, (5/3), 0.1 c. (5/3), 0.1, 0.7, √2, √5 ? 
please help with math
There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so … 
THE HOMEWORK IS DUE TODAY HELP! HELP! PLEASE
There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so … 
math
There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so … 
8th grade algebra
Can you check my answers? 1. 3√20/√4 = 3√(5)(4)/2 = 3(2)√5/2 = 3√5 2. 4√15/√9 = 4√15/3 3. √12/√16 = √4(3)/4 = 2√3/4 = √3/2 4. √10/√5 = √2 
Algebra
1. Simplify the expression: 4√18+5√32 A.45√2 B.32√2 C.116√2 D.9√50 2. Simplify the expression: 7√53√80 A.5√5 B.4√75 C.5 D.4√75 3. Simplify the expression: √21(√3+√14) … 
Algebra  Check My Work
For Question 18 Simplify the Radical Expression ***  My Answer 1.√45 3√5*** 2.√180x^2 6x√5*** 3.√150x^3 k^4 5xk^2√6x*** 4.√21y * 5√49y 35y√21*** 5.(The square root sign applies …